**3. History of crystallography table of contents**



## **4. A translation of the "Introduction" to** *History of Crystallography***<sup>1</sup>**

8 Recent Advances in Crystallography

VOLUME II. THE 19TH CENTURY

others

Foreword

Chapter 3. Hints of a structural crystallography – Kepler 50 Chapter 4. Layered growth and the constancy of crystal angles - Steno 65 Chapter 5. Crystal optics - Bartholinus 86 Chapter 6. Early ideas about crystal growth 95 Chapter 7. Foundational crystallography - Cappeler 110 Chapter 8. Classification – Linnaeus and Buffon 122 Chapter 9. The Russian school - Lomonsov 140 Chapter 10. 17th and 18th Century crystallization theories 158 Chapter 11. Crystal growth - Leblanc and Lovits 177 Chapter 12. Electrical properties of crystals 195 Chapter 13. Mineralogy - Werner 202 Chapter 14. An independent science - Romé de l'Lisle 216 Chapter 15. Häuy's predecessor - Bergman 241 Chapter 16. A theory of crystal structure – Häuy 253 Conclusion 276 References 278 Citations 289 Author index 290

Introduction 5 Chapter 1. The reflecting goniometer - Wollaston 9 Chapter 2. Development of crystal systems – Mohs and Weiss 20 Chapter 3. Morphology of minerals - Breitthaupt, Rose, Neumann, Koksharov, and

Chapter 4. Isomorphism, and polymorphism – Mitscherlich 65 Chapter 5. Crystal optics 78 Chapter 6. Mathematical crystallography 96 Chapter 7. The 32 crystal classes - Hessel, Bravias, and Gadolin 109 Chapter 8. The 14 Bravais lattices 137 Chapter 9. Space groups - Sohncke, Fedorov, Shoenflies, and Barlow 159 Chapter 10. Molecular dissymmetry - Pasteur 180 Chapter 11. Real crystals and complex forms 193 Chapter 12. Physical and chemical crystallography 208 Chapter 13. Universal symmetry principle - Curie 227 Chapter 14. Groth's monument 239 Chapter 15. Morphology of crystals - Goldschmidt 255 Chapter 16. Foundations of modern crystallography - Fedorov 270 Conclusion 303 Citations 306 Author index 317

40

Goethe said, "The history of science is science itself" (Fink, 1991). Crystallography well illustrates his aphorism, at least as judged from its development in textbooks. Indeed, turning the pages of an elementary treatise in crystallography takes us from the simple to the complex following the chronological development of the science of crystals. For instance, the chronology of discoveries in geometrical crystallography mimics the order in which the associated concepts are presented in most textbooks. Pliny the Elder (AD 23 – 79) marveled at the extraordinarily flat faces of quartz crystals: "not even the most skillful lapidary could achieve such a finish" (Healy, 1999). A long time passed before the law of the constancy of interfacial angles was articulated in 17th and 18th centuries by Steno (1638-1686), Henkel (1678-1744), Lomonosov (1711-1765), and Romé de l'Lisle (1736-1790). Häuy (1743-1834) went further with law of rational indices, and the relationship between external shapes and internal structure. Weiss and Mohs deduced the zone law at the start of the 19th Century. Hessel, Bravais, and Gadolin (1828-1892) derived the finite symmetry classes, the 32 crystallographic point groups. Frankenheim (1801-1869), Bravias (1811-1863), and Sohncke (1842-1898) introduced the infinite symmetries of lattices. Fedorov and Schoenflies (1853- 1928) carry us into the 20th Century and modern structural crystallography with derivations of the 230 space groups.

We could reconstruct the development of crystal physics likewise by tracing a path through discovery of double refraction in Iceland spar by Bartholinus (1669), to the correlation of optical and morphological symmetry by Brewster (1781-1868), to the correlation of all physical properties of crystals with symmetry by Neumann (1798-1895), and to the general symmetry principle of Curie (1859-1906) and modern solid state physics.

We thus might conclude that organizing a history of crystallography is a simple task. We need only enumerate in chronological order, and then elaborate on, all the achievements of crystallography. Of course, the situation is more complicated than it appears at first blush. The skeletal historical outlines above are idealized and purged of detours. Bewilderment, the lifeblood of the scientific enterprise, is nowhere in evidence. Such an accounting prejudicially selects only those developments that are organically incorporated into modern crystallography without disturbing the harmony of the imposing edifice. A faithful history of crystallography -- in all its fullness -- muddles the implicit history of the textbooks.

Foremost among the characteristics of crystals that have guided the development of crystallography is the problem presented by the stridently polyhedral shapes of crystals. "Crystals flash forth their symmetry"2 according to Fedorov on the first page of his *Course in Crystallography* (1901). This fact had practical consequences: Agricola (1494-1555) instructed miners to identify minerals through their external "angular figures" (Agricola, 1556, 1950). Yet, Nature's well-facetted crystals presented a clearly defined problem to natural

<sup>1</sup> In order to provide more complete citations, we have added some sources that postdate Shafranovskii.

<sup>2</sup> The English rendering of this phrase was taken from Archard's translation of Shubnikov and Kopstik (1974).

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philosophers that could not be solved without comprehensive geometrical analyses. Cardano (1501-1576) first proposed (1562) that the hexagonality of the rock crystal might arise from an internal structure consisting of densely packed spheres, anticipating Harriot (1560-1621) and Kepler, in part (Shafranovskii, 1975; Kahr, 2011). Ever since, the theoretical and empirical sciences of crystals developed in parallel. Albeit theory outpaced experiment until the 20th Century.

On the slight basis that crystals have geometrical shapes, are homogeneous, and anisotropic, theorists created a breathtaking mathematical crystallography. First articulated were laws that controlled the appearance of crystals of finite point symmetry. Like other mathematical disciplines, the development of theoretical crystallography was strictly logical, led to prediction, and guided subsequent experimental studies. The deduction of crystal classes (Hessel, 1830; Gadolin, 1867) was carried out before many of were illustrated by minerals; of the 32 crystal point groups, Gadolin found only 20 examples in nature. The laws governing crystal point symmetries were then extended to cover the symmetries of infinite crystal lattices. Indeed, at the end of the 19th Century, achievements in mathematical crystallography were so impressive that Fedorov proclaimed that its mathematical character rendered it "one of the most exact sciences" (Fedorov, 1901). Only now have advances in analysis matched those of theory, restoring balance to the science of crystals.

In the middle of 19th Century Frankenheim and Bravais developed the concept of the crystal lattice enumerating the 14 frameworks that form the basis of the modern structural crystallography. "Nature knelt before the hard theory, and the crystals positioned themselves in those classes where they should be according to the geometrical systems of points (space lattices)," expressively wrote Fedorov (1891). The 14 Bravais lattices and the 32 point groups were the constraints between which Fedorov, and independently Schoenflies (1853-1928), deduced in 1890-1891 the 230 possible space groups that restrict the mutual arrangement of building units (atoms, ions, molecules) inside crystals (1891). These farseeing predictions were fully supported by experimental data subsequent to the discovery of X-ray diffraction by von Laue (1912), an achievement that is no less impressive than Mendeleev's expectations of undiscovered chemical elements on the basis of the periodic system. The derivation of the 230 space groups of Fedorov caps our history; it is the pinnacle in development of the classical science of crystallography.

Along the way, sharp conflicts between scientists were provoked. Romé de l'Lisle clashed with Häuy on the relationship between morphology and internal structure. The German physiographical school of Weiss (1780-1856), Mohs (1773-1839), and Naumann (1797-1873), conflicted with theoretical studies by Hessel (1796-1872) and Bravias. Mineralogists Koksharov and Eremeev (1830-1899) fiercely resisted the mathematical generalizations of the Fedorov.

In this history, chapters devoted to the development of important crystallography concepts alternate with chapters devoted to the lives, creative work, and struggles of the greatest crystallographers. Biographical details that inform certain advances are vital in that they color the local character or "microclimate" out of which those advances arose. Accounts of the fate of a discovery, involving the collective acceptance or negation of an idea by many scientists working in disparate countries over centuries, illustrate the global character of the history of crystallography. Experiment and theory drive one another while great currents sweep up individuals whose works and words broaden the stream.

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until the 20th Century.

the Fedorov.

philosophers that could not be solved without comprehensive geometrical analyses. Cardano (1501-1576) first proposed (1562) that the hexagonality of the rock crystal might arise from an internal structure consisting of densely packed spheres, anticipating Harriot (1560-1621) and Kepler, in part (Shafranovskii, 1975; Kahr, 2011). Ever since, the theoretical and empirical sciences of crystals developed in parallel. Albeit theory outpaced experiment

On the slight basis that crystals have geometrical shapes, are homogeneous, and anisotropic, theorists created a breathtaking mathematical crystallography. First articulated were laws that controlled the appearance of crystals of finite point symmetry. Like other mathematical disciplines, the development of theoretical crystallography was strictly logical, led to prediction, and guided subsequent experimental studies. The deduction of crystal classes (Hessel, 1830; Gadolin, 1867) was carried out before many of were illustrated by minerals; of the 32 crystal point groups, Gadolin found only 20 examples in nature. The laws governing crystal point symmetries were then extended to cover the symmetries of infinite crystal lattices. Indeed, at the end of the 19th Century, achievements in mathematical crystallography were so impressive that Fedorov proclaimed that its mathematical character rendered it "one of the most exact sciences" (Fedorov, 1901). Only now have advances in

In the middle of 19th Century Frankenheim and Bravais developed the concept of the crystal lattice enumerating the 14 frameworks that form the basis of the modern structural crystallography. "Nature knelt before the hard theory, and the crystals positioned themselves in those classes where they should be according to the geometrical systems of points (space lattices)," expressively wrote Fedorov (1891). The 14 Bravais lattices and the 32 point groups were the constraints between which Fedorov, and independently Schoenflies (1853-1928), deduced in 1890-1891 the 230 possible space groups that restrict the mutual arrangement of building units (atoms, ions, molecules) inside crystals (1891). These farseeing predictions were fully supported by experimental data subsequent to the discovery of X-ray diffraction by von Laue (1912), an achievement that is no less impressive than Mendeleev's expectations of undiscovered chemical elements on the basis of the periodic system. The derivation of the 230 space groups of Fedorov caps our history; it is the pinnacle

Along the way, sharp conflicts between scientists were provoked. Romé de l'Lisle clashed with Häuy on the relationship between morphology and internal structure. The German physiographical school of Weiss (1780-1856), Mohs (1773-1839), and Naumann (1797-1873), conflicted with theoretical studies by Hessel (1796-1872) and Bravias. Mineralogists Koksharov and Eremeev (1830-1899) fiercely resisted the mathematical generalizations of

In this history, chapters devoted to the development of important crystallography concepts alternate with chapters devoted to the lives, creative work, and struggles of the greatest crystallographers. Biographical details that inform certain advances are vital in that they color the local character or "microclimate" out of which those advances arose. Accounts of

analysis matched those of theory, restoring balance to the science of crystals.

in development of the classical science of crystallography.

The use of crystalline materials by various professionals, further confounds the author of a history of crystallography. Since ancient times minerals guided miners in search of raw materials. Subsequently, the growth of crystals became a part of problem solving in metallurgy, physics, chemistry, and pharmacology, connecting crystallography with many branches of pure and applied science. This prevented crystallography from coalescing as an independent science for a long time. Crystallography was variously considered as a part physics, chemistry, mathematics, or especially mineralogy. In the 19th Century, crystallography was "preparatory mineralogy". Young Fedorov called crystallography "geometrical mineralogy". Even after having placed the capstone on the science of classical crystallography with the derivation of the space groups, Fedorov wrote at the end of his life: "[Crystallography] plays an essential role at the heart of mineralogy and as part of mining science whose primary purpose is utilization of natural resources" (Fedorov, 1955). Only recently has the characterization of crystallography as a "servant of mineralogy" faded. Today even cell biologists, and biomedical researchers embrace crystallography although this aspect of the history of crystallography is not covered herein.

Metzger, it her doctoral dissertation *Genèse de la Science d'Cristaux* (1918), previously considered crystallography's emergence from other sciences. Nevertheless, there is backflow; advances in the aforementioned disciplines draw crystallography back in. For instance, according to Vernadsky, "Crystallography has not been separated from mineralogy. It embraced mineralogy in a new way, entered its foundations and changed it radically…Mineralogy does not need to free itself from the physical sciences. Rather we must build new relationships between crystallography and mineralogy so as to transform the latter" (Vernadsky, 1928). Similar things have been said about the relationship of crystallography to chemistry (Engels, 1954) and to pharmacy (Fabian, 1967).

The changing interrelations among the sciences and their sub-disciplines complicates a reconstruction of the history of crystallography. Important threads must be picked from the vast literature on mineralogy, mathematics, physics, chemistry, metallurgy, medicine, and biology among others disciplines. This extraction requires an enormous amount of time and effort. Obviously, the history of crystallography can be only conditionally likened to a continuous, smooth line. In reality, we face something like a dotted line diving in and out of the general tableaux of the development of science.

So, how shall we write a history of crystallography? We can follow Metzger and little by little separate crystallography from historically related sciences, stressing the increasing independence from other disciplines. Alternatively, we can consider the development of crystallography as a natural structure constrained by the symmetries of regular crystal packing that started with minerals and gradually subsumed a wider spectrum of objects from synthetic molecular crystals to semi-conductors to drugs to proteins. The development

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of crystallography validates both approaches. This happens due to dialectic process of the differentiation and synthesis of the sciences (Figurovsky, 1969). Indeed, specialization of the science of crystals results in great progress; narrow disciplines can probe ever more deeply. On the other hand, increasing contacts among a rising number of allied disciplines obscures the main themes that specifically delineate the development of crystallography.

These ideas fully correspond to the new conceptions of the development of sciences. It is interesting to note that Fedorov stands at the beginning of such a systems approach. In his philosophical treatise "Perfectionism" he wrote: "The scientist is perpetually faced with the generalization of proven laws. The higher the philosophical development of a scientist, the clearer he understands the need to generalize even further because the logic of philosophy requires complete reduction" (Fedorov, 1906). The same ideas expressed more emphatically can be found in his later papers: "Are there true boundaries between sciences? Maybe all the sciences constitute something united and indivisible. Maybe the boundaries of a science, as they are established, represent only artificial constructions adapted to current understanding" (Fedorov, 1917). Thus, we must follow the historically conditioned development of the science of crystals without becoming isolated behind "artificial partitions" established by other disciplines.

Crystallographic phenomenology is emblematic to scientific generalization. Now, scientists often invoke "isomorphic laws" in different fields of science. It is gratifying to witness symmetry laws, firstly discovered in crystals, transferred to other fields of science. The beautiful examples of "isomorphism" underscore the relationship of geometrical crystallography to chemistry; the Steno-Lomonosov-Romé de l'Lisle law of the constancy of crystal angles is "isomorphic" to the law of Proust (1754-1826) on the constancy of composition of "true chemical compounds". Lomonsov's mentor, Henkel, formulated the law of the constancy of crystal angles as follows: "Nature in the confusion of her varied combinations has chosen the structure and external appearance of substances according to their properties and corresponding to external conditions and circumstances. She does not deviate from this rule; she sets a compass and measures the angles establishing one substance for all time." (Marx, 1825). Of his eponymous law, Proust said: "A compound is a privileged product, that Nature has given a constant composition. Nature, even with the intercession of people, never produces a compound without balance in hand; everything is in accord with weight and measure" (Menshutkin, 1937). The similarity in the formulation of this statement with that of Henkel is startling.

The law of the constancy of angles combined with the observation of cleavage phenomena led Häuy to formulate the unique "polyhedral molecules" (crystal structures in modern parlance) for a given crystalline compound. In the 20th Century, Goldschmidt (1888-1947) interpreted this statement as "the primary basis of crystal chemistry" (Goldschmidt, 1937). The thesis of Häuy combined with Steno's law is the crystallographic analogue of the Proust's generalization in chemistry. The law of rational indices in crystals by Häuy is "isomorphous" to the basic law of chemistry, Dalton's (1766-1844) law of multiple proportions. Obviously, the older crystallographic laws played some role in establishing of latter ones. Thus, once again we see the impossible task of the historian keen to separate unadulterated crystallography from closely related disciplines of physics, chemistry, and mineralogy.

Periodization, the subdivision of a long history into stages of development, provides further practical problems for the historian. Lenin (1870-1924) provides a general guide: "From living contemplation to abstract thinking *and then to practice* – this is a dialectic way in perception of *truth*, perception of objective reality" (Lenin, 1967). These words agree well with a statement by Fedorov: "When the nearest practical consequences of a given theory become known, we acquire the power to control Nature…the task of any science is to obtain such a power. Therefore, everything that gives this power is scientifically true" (Fedorov, 1904).

According to Kedrov (1903-1985), there are three main stages in the development of any science: (1) empirical fact gathering, (2) theory and explanation, and (3) prognostication (Kedrov, 1971). In the history of crystallography, we can see all three periods. For example, previously, with Grigoriev, we divided the history of Russian mineralogy and crystallography into four stages: narrative-descriptive, exact-descriptive, theoretical, and synthetic (Grigoriev, Shafranovskii, 1949). To a certain extent this division agrees with Kedrov if the two descriptive stages are aligned with his empirical stage. While mindful of the dual theoretical and practical development of crystallography, we recognize that a strict division into stages is impossible. In fact, Kedrov admits the conditional character of his divisions. In Russian crystallography, these periods are intertwined, overlapped, and sometimes inverted. Sometimes all three Kedrov stages can be identified in the activity of one and the same scientist. Nevertheless, stages are evident when we take a course-grained, centuries-wise perspective of the most significant achievements that carried the science forward: rules of morphology by Steno (1669), formulation of descriptive and theoretical crystallography by Romé de l'Lisle and Häuy (1783-1784), the mathematical inventions of Fedorov (1881-1919). In the 20th Century we have to acknowledge two "great revolutions in crystallography" as they were called by academician Belov (1891-1982): the epochal discovery of X-ray diffraction by von Laue (1912) and revolutionary developments in the growth of technically important single crystals in the 1950s and1960s (Belov, 1972).

In this work, for operational purposes, we distinguish four periods in the history of crystallography:

1. Prehistory, from ancient times to Steno;

12 Recent Advances in Crystallography

partitions" established by other disciplines.

of this statement with that of Henkel is startling.

of crystallography validates both approaches. This happens due to dialectic process of the differentiation and synthesis of the sciences (Figurovsky, 1969). Indeed, specialization of the science of crystals results in great progress; narrow disciplines can probe ever more deeply. On the other hand, increasing contacts among a rising number of allied disciplines obscures

These ideas fully correspond to the new conceptions of the development of sciences. It is interesting to note that Fedorov stands at the beginning of such a systems approach. In his philosophical treatise "Perfectionism" he wrote: "The scientist is perpetually faced with the generalization of proven laws. The higher the philosophical development of a scientist, the clearer he understands the need to generalize even further because the logic of philosophy requires complete reduction" (Fedorov, 1906). The same ideas expressed more emphatically can be found in his later papers: "Are there true boundaries between sciences? Maybe all the sciences constitute something united and indivisible. Maybe the boundaries of a science, as they are established, represent only artificial constructions adapted to current understanding" (Fedorov, 1917). Thus, we must follow the historically conditioned development of the science of crystals without becoming isolated behind "artificial

Crystallographic phenomenology is emblematic to scientific generalization. Now, scientists often invoke "isomorphic laws" in different fields of science. It is gratifying to witness symmetry laws, firstly discovered in crystals, transferred to other fields of science. The beautiful examples of "isomorphism" underscore the relationship of geometrical crystallography to chemistry; the Steno-Lomonosov-Romé de l'Lisle law of the constancy of crystal angles is "isomorphic" to the law of Proust (1754-1826) on the constancy of composition of "true chemical compounds". Lomonsov's mentor, Henkel, formulated the law of the constancy of crystal angles as follows: "Nature in the confusion of her varied combinations has chosen the structure and external appearance of substances according to their properties and corresponding to external conditions and circumstances. She does not deviate from this rule; she sets a compass and measures the angles establishing one substance for all time." (Marx, 1825). Of his eponymous law, Proust said: "A compound is a privileged product, that Nature has given a constant composition. Nature, even with the intercession of people, never produces a compound without balance in hand; everything is in accord with weight and measure" (Menshutkin, 1937). The similarity in the formulation

The law of the constancy of angles combined with the observation of cleavage phenomena led Häuy to formulate the unique "polyhedral molecules" (crystal structures in modern parlance) for a given crystalline compound. In the 20th Century, Goldschmidt (1888-1947) interpreted this statement as "the primary basis of crystal chemistry" (Goldschmidt, 1937). The thesis of Häuy combined with Steno's law is the crystallographic analogue of the Proust's generalization in chemistry. The law of rational indices in crystals by Häuy is "isomorphous" to the basic law of chemistry, Dalton's (1766-1844) law of multiple proportions. Obviously, the older crystallographic laws played some role in establishing of

the main themes that specifically delineate the development of crystallography.


A finer grained division into stages requires accounting of the related scientific disciplines: geology (Tikhomirov & Khain, 1956; Gordeev, 1967; Batyushkova, 1973), mineralogy

(Povarennyh, 1962), physics (Dorfman, 1974), and chemistry (Figurovsky, 1969) among others.
